*Due:* 10:30 p.m., Tuesday, 9 October 2012

*Summary:*
In this assignment, you will use turtles to explore mechanisms
for constructing images based on a variety of polygons.
Our focus will be on using lists, iteration, and anonymous procedures
as ways to work with the turtle model.

*Purposes:* To give you more experience with the
turtle model. To give you more comfort with anonymous procedures.
To explore the complexities possible from simple operations.

*Expected Time:*
Two to four hours.

*Collaboration:*
We encourage you to work in groups of size two. You may, however,
work alone or work in a group of size three.

*Submitting:*
Email your answer to `<grader-151-02@cs.grinnell.edu>`

. The title of your email
should have the form ** CSC151-02 Assignment 5: Polygons** and
should contain your answers to all parts of the assignment. Scheme code
should be in the body of the message.

*Warning:*
So that this assignment is a learning experience for everyone, we may
spend class time publicly critiquing your work.

Write a procedure, `(`

, that uses a turtle to draw a
regular polygon with the specified number of sides, with each side of
the specified length.
`turtle-polygon!`

`turtle`

`side-length`

* sides*)

*Important:* Your procedure must use the turtle's
existing position and orientation when it starts, returning the
turtle to its original position and orientation when it completes.
Your procedure must *not* change the turtle's
brush or color.

*Hint:* Use `repeat`

. The
turtle must turn a total of 360 degrees to return to its original
angle.

For example,

`(turtle-polygon! t 100 3)`

`(turtle-polygon! t 100 4)`

`(turtle-polygon! t 60 5)`

`(turtle-polygon! t 40 6)`

Write a procedure, `(`

, that draws the given number
of copies of the specified polygon by calling your
`turtle-spin-polygon!`

`turtle`

`side-length`

`sides`

`angle`

* copies*)

`turtle-polygon!`

procedure,
with the turtle turned an angle
of `angle`

*Important:* As in problem one, your procedure
should start the turtle from its current position and orientation,
returning the turtle to its original position and orientation when
the procedure is complete.

For example,

`(turtle-spin-polygon! t 50 4 15 10)`

`(turtle-spin-polygon! t 50 4 20 5)`

`(turtle-spin-polygon! t 50 4 5 20)`

`(turtle-spin-polygon! t 50 4 -30 5)`

Write a procedure, `(`

, that draws the given number
of copies of the specified polygon, with each copy drawn with a
side length `turtle-scale-polygon!`

`turtle`

`initial-side-length`

`sides`

`scale-factor`

* copies*)

`scale-factor`

For example, if the initial side length is ten, and the scale factor is two, this procedure would draw polygons with side lengths 10, 20, 40, 80, 160, ....

Similarly, if the initial side length is 100, and the scale factor is 0.9, the procedure would draw polygons with side lengths 100, 90, 81, 72.9, ....

*Important:* As in the previous problems, your
procedure must start from and return the turtle to its original
position and orientation.

*Hint:* The `expt`

function
will be useful for finding the ratio of each polygon's side length to
the original side length. For example, for scale factor two, the
ratios would be 1, 2, 4, 8, 16, 32, and so on.

Here are some visual issues.

`(turtle-scale-polygon! t 1 5 2 8)`

`(turtle-scale-polygon! t 1 5 1.2 30)`

`(turtle-scale-polygon! t 100 5 0.9 20)`

A potential deficiency of each of the prior two procedures is that multiple polygons are joined at a vertex. The problem is, of course, that our basic polygon procedure draws polygons starting at a particular point, rather than centered at a certain point.

Copy the following procedure to your definitions pane.

(define turtle-centered-polygon! (lambda (turtle radius sides) (let ((interior-angle (/ (* 180 (- sides 2)) sides))) (turtle-up! turtle) (turtle-forward! turtle radius) (turtle-down! turtle) (turtle-turn! turtle (- 180 (/ interior-angle 2))) (turtle-polygon! turtle (* 2 radius (sin (/ pi sides))) sides) (turtle-turn! turtle (/ interior-angle 2)) (turtle-up! turtle) (turtle-forward! turtle radius) (turtle-turn! turtle 180) (turtle-down! turtle))))

Experiment with this procedure to learn what it does. (Hint: Note that this
procedure assumes your `turtle-polygon!`

draws the
first side of the polygon before turning.)

a. Document this procedure using the 6Ps.

b. Explain why each expression in the procedure's body is necessary to achieve the result that you see. That is, explain each step of the algorithm in English.

*Hint:* You may find it useful to comment out
each expression using a semicolon, one at a time, to see how the
result of leaving out that expression differs from the desired
result.)

Write the procedure
`(`

.
`turtle-spin-centered-polygon!`

`turtle`

`radius`

`sides`

`angle`

* copies*)

This procedure should be very similar to
`turtle-spin-polygon!`

from problem 2, except that it will call
the `turtle-centered-polygon!`

procedure from Problem 4 instead of your
`turtle-polygon!`

procedure from Problem 1.

Your first polygon procedure draws the outline of a polygon. What if, instead of drawing a simple polygon, we wanted to position the turtle at each of the vertices of a polygon as preparation for some other action? If that other action is provided in the form of a procedure that takes a turtle as a parameter and leaves the turtle in the same position it started in, the task is similar to our original polygon creating procedure.

Write a procedure `(`

,
that applies the procedure `turtle-action-polygon!`

`turtle`

`side-length`

`sides`

* action!*)

`action!`

`turtle`

*Important:* As in the previous problems, your
procedure must return the turtle to its original position and
orientation.

`(turtle-action-polygon! t 65 5 (lambda (turtle) (turtle-spin-polygon! turtle 20 4 15 5)))`

`(turtle-action-polygon! t 8 50 (lambda (turtle) (turtle-polygon! turtle 5 20 )))`

(a) Write a program that systematically generates an interesting image composed of a series of polygons. You should purposefully choose a background color and the color(s) of the polygons to produce some effect on the viewer.

You may call the procedures you wrote in problems 1-6 with
carefully chosen parameters to produce a complex image, or you may
write and document new procedures (such as one that both spins
*and* scales progressively). In addition to
colors, you may also wish to choose particular brushes.In addition
to scaling and spinning polygons, you might think about varying
the sizes and positions of the polygons in other ways, or even
changing the number of sides between different polygons.

(b) Write a short paragraph explaining what color scheme you chose and why, drawing on appropriate terminology about design and color.

We will judge your solutions on their correctness, their conciseness, and their cleverness. We will also judge your solution to problem 7 on its creativity and on the clarity of your intentions.

Copyright © 2007-2012 Janet Davis, Matthew Kluber, Samuel A. Rebelsky, and Jerod Weinman. (Selected materials copyright by John David Stone and Henry Walker and used by permission.)

This material is based upon work partially supported by the National Science Foundation under Grant No. CCLI-0633090. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons Attribution-NonCommercial 2.5 License .